PHYS 151 Midterm #1
100 points total
Due Friday, September 25 at 5:00 PM
1. (8 pts) A bug moves from an initial position h1, −4i m to a final position h−7, 3i m in half a minute.
At the initial position the bug had a velocity of h1, 2i m/s and at the final location it had a velocity
of h2, 1i m/s. Determine (a) the average velocity and (b) the average acceleration during the trip.
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2. (12 pts) Milton is driving his brand new Subaru BRZ sports car at 60 miles per hour when he sees
a red light up ahead. He applies the brakes and comes to a stop after traveling 35 meters.
a) What is the car’s acceleration in SI units?
b) What fraction of the gravitational acceleration g is this?
c) How much time does it take Milton to come to rest?
*You may want to know that 1 mile = 1.609 km
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3. (12 pts) The velocity vs. time profile of an object is plotted in the figure below.
a) Describe in your own words the object’s overall motion.
b) Draw the acceleration vs. time profile of this object.
c) Draw the displacement vs. time profile of this object.
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4. (12 pts) Jack and Jill finish their physics midterm exam and decide to take a spontaneous road trip.
Their trip involves the following movements:
First they go 35 miles, 70◦ south of east.
Then they go 18 miles, due east.
Lastly, they go 42 miles, 15◦ north of east.
Jack’s car breaks down after the last leg of the trip. a) Draw a picture to represent the overall
displacement of the students. b) How far and in what direction are Jack and Jill from campus upon
breaking down?
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5. (15 pts) A major league baseball player hits a fly ball. The ball leaves the bat with a velocity of 44
m/s at an angle of 67◦ above the horizontal. How far from home plate does the center fielder need
to stand if he is going to catch the ball at the same height from which it was hit?
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6. (18 pts) An archer shoots an arrow at an angle 25◦ above the horizontal. At the peak of its trajectory,
the arrow just barely clears a 42 m high oak tree. a) How fast was the arrow going when it left the
bow? (Assume it was shot from a height of 1.0 m above the ground.) b) How far away is the archer
from the tree?
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7. (15 pts) Pete and Susie are racing motorcycles on a straight section of highway. At time t = 0, Pete
passes Susie. At that time, Pete has a speed of 27 m/s and Susie has a speed of 20 m/s. One second
later, Susie begins to accelerate at a rate of 1.5 m/s2 . a) If she maintains this acceleration, at what
time will Susie once again overtake Pete? b) How far have they moved in this time?
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~ = h4, 5i and vector B
~ = h1, 3i. Draw the two vectors.
8. (8 pts) You are given two vectors: vector A
~
~
What is the measure, in degrees, of the angle between vector A and vector B?
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